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Modular, log canonical, and tropical compactifications

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Speaker: Eugene Tevelev, University of Texas at Austin
Location: 1147 MSB
Start time: Tue, Feb 7 2006, 4:10PM

The celebrated moduli space of stable curves of Grothendieck, Knudsen, and Mumford admits a straightforward generalization in all dimensions: the moduli space of stable pairs introduced by Kollar, Shepherd-Barron, and Alexeev. Their construction is not effective and relies on the Minimal Model Program. Using the classical example of a cubic surface with 27 lines, I'll describe joint work with Hacking and Keel where we construct the moduli space of stable Del Pezzo surfaces and describe its boundary using non-archimedean amoebas. This is one instance of the beautiful connection between the Mori theory and the "tropical geometry".